Problem: Simplify the following expression: $y = \dfrac{10a^2 + 80a + 150}{a + 5} $
Explanation: First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $10$ , so we can rewrite the expression: $ y =\dfrac{10(a^2 + 8a + 15)}{a + 5} $ Then we factor the remaining polynomial: $a^2 + {8}a + {15} $ ${5} + {3} = {8}$ ${5} \times {3} = {15}$ $ (a + {5}) (a + {3}) $ This gives us a factored expression: $\dfrac{10(a + {5}) (a + {3})}{a + 5}$ We can divide the numerator and denominator by $(a - 5)$ on condition that $a \neq -5$ Therefore $y = 10(a + 3); a \neq -5$